MGF 1106

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MGF 1106. Test 3 Review and Practice Solutions. You will need to have your own calculator for the test. You may not share calculators or use any type of communication device in place of a calculator.

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MGF 1106

Test 3 Review

and

Practice Solutions

You will need to have your own calculator for the test.

• You may not share calculators or use any type of communication device in place of a calculator.
• Tests may not be made up for any reason other than a mandatory school – sponsored activity for which you must miss class.
• If you miss one test for any other reason, your final exam score will be substituted for that test. A second missed test is a zero. No homework bonuses are awarded on a test when the final exam is substituted or you receive a zero on a missed test.

1) John is considering being a clown at a costume party. At the costume shop, he is told that he can choose one of four colors for the pants, one of three colors for the shirt. Additionally, he must choose whether to wear a big red nose or not and whether his hat should be round or triangular. How many different clown costume possibilities are there?

2) Evaluate: You will not be able to enter this expression (as it is written) on your calculator. Doing so will produce an error and writing “no solution” or “error” will result in no credit being given. Simplify the expression first and then use your calculator.

3) A club with twenty members is to choose four officers – president, vice−president, treasurer, and secretary. If each office is to be held by one person and no person can hold more than one office, in how many ways can those offices be filled?

OR

20P4 =

5) Determine if each problem involves permutations or combinations. You do not have to solve the problems.

a) A yogurt store has 15 different flavors of yogurt. In how many ways can you select 3 flavors to be placed into a 3 – flavor sundae bowl?

Combination – the order of the flavors does not matter

b) James is making a scrapbook of his senior year. He has 40 photos to choose from. The scrapbook has 25 numbered pages and each page will contain one photo. In how many ways can he arrange the photos in the scrapbook?

Permutation – the book is numbered and the photos will be placed in a certain order

6) Becka’s homeroom teacher must select a group of four students at random to go to the library to help clean up after a weekend flood. If there are 18 students in Becka’s homeroom, how many different groups of students are possible?

7) A science club consists of 18 freshmen and 15 sophomores. In how many ways can 12 freshmen and 10 sophomores be chosen to go on a field trip?

8) Suppose an eight−sided die is rolled. The sides of the dice are Find probability of rolling:

a) a 7

b) a number greater than 5

c) a number less than 9

d) a number greater than 10

9) Seven movies {A, B, C, D, E, F, G} are being shown in a movie marathon. Find the probability that film C will be shown first, film A next–to–last, and film E last.

1

1

4

3

2

1

1

A

E

C

10) A committee of four people is to be selected from six students and four faculty members. Find the probability that two are students and two are faculty members.

11) (page 646: 41) The table below shows the educational attainment of the U.S. population, ages 25 and over, in 2007. Use the data in the table (expressed in millions) to determine the find the probability that a randomly selected American has not completed 4 years of college.

12) (page 646: 45) The table below shows the educational attainment of the U.S. population, ages 25 and over, in 2007. Use the data in the table (expressed in millions) to determine the find the probability that a randomly selected American has completed 4 years of high school only or is a man.

13) One card is randomly drawn from a standard deck of 52 cards. Find the odds in favor of selecting a queen.

14) The members of the chemistry club decide to play a game. To begin, everyone will write their major on a slip of paper and place it in the hat. There are three math majors, five science majors, and two education majors present. Suppose one slip of paper is drawn out of the hat and replaced. A second slip of paper is drawn out of the hat and replaced and finally a third slip of paper is drawn out and replaced. Find the following probabilities

a) the probability of drawing a math major, then a science major, then an education major.

b) the probability of drawing a math major, then another math major, then a science major.

c) the probability of drawing three education majors in a row

15) The members of the chemistry club decide to play a game. To begin, everyone will write their major on a slip of paper and place it in the hat. There are three math majors, five science majors, and two education majors present. Suppose one slip of paper is drawn out of the hat and not replaced. A second slip of paper is drawn out of the hat and not replaced and finally a third slip of paper is drawn out and not replaced. Find the following probabilities.

a) the probability of drawing a math major, then a science major, then an education major.

b) the probability of drawing a math major, then another math major, then a science major.

c) the probability of drawing three education majors in a row

16) A charity is holding a raffle and sells 1000 raffle tickets for \$2 each. One of the tickets will be selected to win a grand prize of \$1000. Two other tickets will be selected to win consolation prizes of \$50 each. Find the expected value if you buy a raffle ticket. Be sure to use the table below.

17) Students were asked the question, “How many hours of television do you watch on a weekly basis?” The answers are summarized in the stem and leaf plot below. How many students watch at least 28 hours of television per week?

Seven students watch at least 28 hours of television per week.

20) Find the standard deviation.

You will have to fill in the table to receive full credit on the test.

MGF 1106

Extra Practice Problems

1) A popular brand of pen comes in red, green, blue, or black ink. The writing tip can be chosen from extra bold, bold, regular, fine, or micro. How many different choices of pen do you have with this brand?

1) A popular brand of pen comes in red, green, blue, or black ink. The writing tip can be chosen from extra bold, bold, regular, fine, or micro. How many different choices of pen do you have with this brand?

2) Evaluate: You will not be able to enter this expression (as it is written) on your calculator. Doing so will produce an error and writing “no solution” or “error” will result in no credit being given. Simplify the expression first and then use your calculator.

2) Evaluate: You will not be able to enter this expression (as it is written) on your calculator. Doing so will produce an error and writing “no solution” or “error” will result in no credit being given. Simplify the expression first and then use your calculator.

3) You are scheduling television shows for the campus cable channel. You have 13 shows to choose from and six consecutive time slots. How many different programming schedules can be arranged?

3) You are scheduling television shows for the campus cable channel. You have 13 shows to choose from and six consecutive time slots. How many different programming schedules can be arranged?

1235520

OR

13P6 =

Eli needs to select a new password for his phone. He has a choice of 26 letters and 10 numbers for each digit of the password. How many different eight – digit passwords can be formed?

Eli needs to select a new password for his phone. He has a choice of 26 letters and 10 numbers for each digit of the password. How many different eight – digit passwords can be formed?

Permutation – order matters in a password

6) From the 20 CD’s in your collection, you plan to give 3 to your best friend. How many different sets of 3 CD’s are possible?
6) From the 20 CD’s in your collection, you plan to give 3 to your best friend. How many different sets of 3 CD’s are possible?

7) A political discussion group consists of 12 Republicans and 8 Democrats. In how many ways can 5 Republicans and 4 Democrats be selected to attend a conference?

7) A political discussion group consists of 12 Republicans and 8 Democrats. In how many ways can 5 Republicans and 4 Democrats be selected to attend a conference?

8) A fair coin is tossed three times in succession. The set of equally likely outcomes is {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

b) the same outcome on all three tosses

c) a head or a tail on each of the three tosses

d) four tails

8) A fair coin is tossed three times in succession. The set of equally likely outcomes is {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

b) the same outcome on all three tosses

c) a head or a tail on each of the three tosses

d) four tails

9) Seven movies {A, B, C, D, E, F, G} are being shown in a movie marathon. Find the probability that film A will be first, film C will be third, and either film F or G will be last.

9) Seven movies {A, B, C, D, E, F, G} are being shown in a movie marathon. Find the probability that film A will be first, film C will be third, and either film F or G will be last.

2

1

4

1

3

2

1

C

F or G

A

10) A committee of four people is to be selected from six students and four faculty members. Find the probability that all are students.

10) A committee of four people is to be selected from six students and four faculty members. Find the probability that all are students.

11) (page 646: 42) The table below shows the educational attainment of the U.S. population, ages 25 and over, in 2007. Use the data in the table (expressed in millions) to determine the find the probability that a randomly selected American has not completed 4 years of high school.

11) (page 646: 42) The table below shows the educational attainment of the U.S. population, ages 25 and over, in 2007. Use the data in the table (expressed in millions) to determine the find the probability that a randomly selected American has not completed 4 years of high school.

12) (page 646: 46) The table below shows the educational attainment of the U.S. population, ages 25 and over, in 2007. Use the data in the table (expressed in millions) to determine the find the probability that a randomly selected American has completed 4 years of high school only or is a woman.

12) (page 646: 46) The table below shows the educational attainment of the U.S. population, ages 25 and over, in 2007. Use the data in the table (expressed in millions) to determine the find the probability that a randomly selected American has completed 4 years of high school only or is a woman.

13) One card is randomly drawn from a standard deck of 52 cards. Find the odds against selecting a queen.
13) One card is randomly drawn from a standard deck of 52 cards. Find the odds against selecting a queen.

14) The members of the chemistry club decide to play a game. To begin, everyone will write their major on a slip of paper and place it in the hat. There are three math majors, five science majors, and two education majors present. Suppose one slip of paper is drawn out of the hat and replaced. A second slip of paper is drawn out of the hat and replaced and finally a third slip of paper is drawn out and replaced. Find the probability of drawing three science majors in a row.

14) The members of the chemistry club decide to play a game. To begin, everyone will write their major on a slip of paper and place it in the hat. There are three math majors, five science majors, and two education majors present. Suppose one slip of paper is drawn out of the hat and replaced. A second slip of paper is drawn out of the hat and replaced and finally a third slip of paper is drawn out and replaced. Find the probability of drawing three science majors in a row.

15) The members of the chemistry club decide to play a game. To begin, everyone will write their major on a slip of paper and place it in the hat. There are three math majors, five science majors, and two education majors present. Suppose one slip of paper is drawn out of the hat and not replaced. A second slip of paper is drawn out of the hat and not replaced and finally a third slip of paper is drawn out and not replaced. Find the probability of drawing three science majors in a row.

15) The members of the chemistry club decide to play a game. To begin, everyone will write their major on a slip of paper and place it in the hat. There are three math majors, five science majors, and two education majors present. Suppose one slip of paper is drawn out of the hat and not replaced. A second slip of paper is drawn out of the hat and not replaced and finally a third slip of paper is drawn out and not replaced. Find the probability of drawing three science majors in a row.

16) A charity is holding a raffle and sells 500 raffle tickets for \$1 each. One of the tickets will be selected to win a grand prize of \$300. Five other tickets will be selected to win consolation prizes of \$5 each. Find the expected value if you buy a raffle ticket. Be sure to use the table below.

16) A charity is holding a raffle and sells 500 raffle tickets for \$1 each. One of the tickets will be selected to win a grand prize of \$300. Five other tickets will be selected to win consolation prizes of \$5 each. Find the expected value if you buy a raffle ticket. Be sure to use the table below.

17) Students were asked the question, “How many hours of television do you watch on a weekly basis?” The answers are summarized in the stem and leaf plot below. How many students watch less than 10 hours of television per week?

17) Students were asked the question, “How many hours of television do you watch on a weekly basis?” The answers are summarized in the stem and leaf plot below. How many students watch less than 10 hours of television per week?

Four students watch less than 10 hours of television per week.

You will have to fill in the table to receive full credit on the test.